Theory of percolation and tunneling regimes in nanogranular metal films

Nanogranular metal composites, consisting of immiscible metallic and insulating phases deposited on a substrate, are characterized by two distinct electronic transport regimes depending on the relative amount of the metallic phase. At sufficiently large metallic loadings, granular metals behave as percolating systems with a well-defined critical concentration above which macroscopic clusters of physically connected conductive particles span the entire sample. Below the critical loading, granular metal films are in the dielectric regime, where current can flow throughout the composite only via hopping or tunneling processes between isolated nanosized particles or clusters. In this case transport is intrinsically non-percolative in the sense that no critical concentration can be identified for the onset of transport. It is shown here that, although being very different in nature, these two regimes can be described by treating percolation and hopping on equal footing. By considering general features of the microstructure and of the electrical connectedness, the concentration dependence of the dc conductivity of several nanogranular metal films is reproduced to high accuracy within an effective medium approach. In particular, fits to published experimental data enable us to extract the values of microscopic parameters that govern the percolation and tunneling regimes, explaining thus the transport properties observed in nanogranular metal films.Comment: 11 pages, 8 figures + Supplemental material with 5 figure

Spin-orbit scattering in d-wave superconductors

When non-magnetic impurities are introduced in a d-wave superconductor, both thermodynamic and spectral properties are strongly affected if the impurity potential is close to the strong resonance limit. In addition to the scalar impurity potential, the charge carriers are also spin-orbit coupled to the impurities. Here it is shown that (i) close to the unitarity limit for the impurity scattering, the spin-orbit contribution is of the same order of magnitude than the scalar scattering and cannot be neglected, (ii) the spin-orbit scattering is pair-breaking and (iii) induces a small id_xy component to the off-diagonal part of the self-energy.Comment: 9 pages, 3 postscript figures, euromacr.tex-europhys.sty, submitted to Europhysics Letter

Large polaron formation induced by Rashba spin-orbit coupling

Here the electron-phonon Holstein model with Rashba spin-orbit interaction is studied for a two dimensional square lattice in the adiabatic limit. It is demonstrated that a delocalized electron at zero spin-orbit coupling localizes into a large polaron state as soon as the Rashba term is nonzero. This spin-orbit induced polaron state has localization length inversely proportional to the Rashba coupling $\gamma$, and it dominates a wide region of the $\gamma$-$\lambda$ phase diagram, where $\lambda$ is the electron-phonon interaction.Comment: 5 pages, 3 figures, version as publishe

Dimensional effects on the tunneling conductivity of gold-implanted nanocomposite films

We study the dependence of the electrical conductivity on the gold concentration of Au-implanted polymethylmethacrylate (PMMA) and alumina nanocomposite thin films. For Au contents larger than a critical concentration, the conductivity of Au-PMMA and Au-alumina is well described by percolation in two dimensions, indicating that the critical correlation length for percolation is larger than the thickness of the films. Below the critical loading, the conductivity is dominated by tunneling processes between isolated Au particles dispersed in PMMA or alumina continuous matrices. Using an effective medium analysis of the tunneling conductivity, we show that Au-PMMA behaves as a tunneling system in two dimensions, as the film thickness is comparable to the mean Au particle size. On the contrary, the conductivity of Au-alumina films is best described by tunneling in three dimensions, although the film thickness is only a few times larger than the particle size. We interpret the enhancement of the effective dimensionality of Au-alumina films in the tunneling regime as due to the larger film thickness as compared to the mean interparticle distances.Comment: 7 pages, 7 figure

Spin susceptibility in small Fermi energy systems: effects of nonmagnetic impurities

In small Fermi energy metals, disorder can deeply modify superconducting state properties leading to a strong suppression of the critical temperature $T_c$. In this paper, we show that also normal state properties can be seriously influenced by disorder when the Fermi energy $E_{\rm F}$ is sufficiently small. We calculate the normal state spin susceptibility $\chi$ for a narrow band electron-phonon coupled metal as a function of the non-magnetic impurity scattering rate $\gamma_{\rm imp}$. We find that as soon as $\gamma_{\rm imp}$ is comparable to $E_{\rm F}$, $\chi$ is strongly reduced with respect to its value in the clean limit. The effects of the electron-phonon interaction including the nonadiabatic corrections are discussed. Our results strongly suggest that the recent finding on irradiated MgB$_2$ samples can be naturally explained in terms of small $E_{\rm F}$ values associated with the $\sigma$-bands of the boron plane, sustaining therefore the hypothesis that MgB$_2$ is a nonadiabatic metal.Comment: 7 pages, 6 eps figures, to appear on Eur. Phys. J.

The small polaron crossover: comparison between exact results and vertex correction approximation

We study the crossover from quasi free electron to small polaron in the Holstein model for a single electron by means of both exact and self-consistent calculations in one dimension and on an infinite coordination lattice. We show that the crossover occurs when both strong coupling and multiphonon conditions are fulfilled leading to different relevant coupling constants in adiabatic and anti-adiabatic region of the parameters space. We also show that the self-consistent calculations obtained by including the first electron-phonon vertex correction give accurate results in a sizeable region of the phase diagram well separated from the polaronic crossover.Comment: 6 pages, revtex (europhys.sty,euromacr.tex); 3 postscript figure